Question 41·SAT Desmos Regression Practice·Problem Solving and Data Analysis

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The scatterplot above shows the relationship between practice hours ( $x$ ) and test score ( $y$ ). A line of best fit is also shown.

For how many of the 11 data points does the line of best fit predict a greater test score than the actual test score?

A line of best fit gives a predicted score, while each dot gives an actual score. Prediction greater than actual means the dot is below the line at the same practice time. Read the scatterplot directly and count those dots. Don’t count a dot above the line, even if another dot at that practice time is below it.

Hints

Hint 1
At a given practice time, the predicted score is the height of the line. The actual score is the height of the dot. Which dot is lower when you compare the two at the same $x$ -value?
Hint 2
Look at the two dots at $x=1$ . Only one is below the line. Check other practice times the same way, then count the dots below.

Step-by-step

Count the dots below the line
Step 1
Match “greater prediction” to a position on the graph
No Desmos needed. Read the dots and the line directly from the scatterplot. At $x=1$ , the line predicts $y=4$ . The dot $(1,3)$ is below that prediction, while $(1,5)$ is above it. Each dot is an actual score, so count a dot only when it sits below the line at the same practice time.
Step 2
Count every qualifying dot
Scan the graph for dots below the line: $(1,3)$ , $(2,4)$ , $(4,6)$ , $(6,8)$ , and $(7,9)$ . There are $5$ data points whose actual scores are less than the line’s predictions. Choice B.

Question 41·SAT Desmos Regression Practice·Problem Solving and Data Analysis

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

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